As I understand it, paramagnetism is similar in its short-term effect to ferromagnetism (spins of the electrons line up with the magnetic field, etc.), though apparently the effect is weaker. What is it exactly that determines whether an atom or molecule is ferromagnetic versus paramagnetic, and why is the paramagnetic effect weaker?

2 Answers
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Ferromagnetism isn't a property of a single atom or molecule, but rather of the crystalline structure of a given material. It emerges due to alignment of magnetic moments of neighboring atoms in the crystalline structure.

This is why ferromagnetic properties disappear above Curie temperature when alignment of magnetic moments of the atoms begins to decrease.

Properties of the crystalline structure are also the reason why some materials with high concentration of iron are ferromagnetic while others aren't. For example, stainless steel with austenite crystalline structure is a nonmagnetic material, while steel with martensite or ferrite structure is ferromagnetic.

It may depend, but generally ferromagnetism originates from the exchange interaction. If due to some reason exchange interaction "works", you end up with magnetic structure: ferromagnetic, antiferromagnetic, etc. If magnetic ions do not feel each other enough, you end up with paramagnetic. It is not the property of the atom or molecule. It is a property of the structure these atoms form.